Complex filters may be useful in a number of applications, such as RF devices. For example, a receiver may use one or more complex filters to reduce noise or filter out adjacent channels. In addition, complex filters may be used to accept a complex signal and separate the real part of the signal from the imaginary part of the signal.
Circuits that act as complex filters may generate complex poles. A complex pole may be useful in circuits that filter quadrature signals, for example, to provide an asymmetric response about DC. Circuits with complex poles may generate quadrature signals from a single signal and perform amplitude/phase filtering of the quadrature signals. The quadrature signals may be generated by quadrature downconversion or in preparation for quadrature upconversion.
Several techniques exist for generating a single complex pole. For example, cross coupling may be used between pairs of real poles. Another technique involves converting a pair of ladder-derived real filters into a frequency-shifted complex filter by using cross coupling between the real filters. In both techniques described, frequency-independent cross coupling and single real poles are used.